Defining parameters
Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8100.ba (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 300 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Sturm bound: | \(3240\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8100, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6576 | 2912 | 3664 |
Cusp forms | 6384 | 2848 | 3536 |
Eisenstein series | 192 | 64 | 128 |
Decomposition of \(S_{2}^{\mathrm{new}}(8100, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8100, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)